Question: Daniel is 9 years younger than Ben. For the last four years, Ben and Daniel have been going to the same school. Seven years ago, Ben was 4 times as old as Daniel. How old is Ben now?
Explanation: We can use the given information to write down two equations that describe the ages of Ben and Daniel. Let Ben's current age be $b$ and Daniel's current age be $d$ The information in the first sentence can be expressed in the following equation: $b = d + 9$ Seven years ago, Ben was $b - 7$ years old, and Daniel was $d - 7$ years old. The information in the second sentence can be expressed in the following equation: $b - 7 = 4(d - 7)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $b$ , it might be easiest to solve our first equation for $d$ and substitute it into our second equation. Solving our first equation for $d$ , we get: $d = b - 9$ . Substituting this into our second equation, we get the equation: $b - 7 = 4($ $(b - 9)$ $ -$ $ 7)$ which combines the information about $b$ from both of our original equations. Simplifying the right side of this equation, we get: $b - 7 = 4b - 64$ Solving for $b$ , we get: $3 b = 57$ $b = 19$.